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Living markup — invented sample
Companion template
This page is not a textbook. It shows the markers tomorrow’s uploads should use: Vortex chain, tool, poor explanation + rewrite, fake task → real job. Sample topic: counting lanterns on a fence (made up).
0. Vortex chain (required Helper beat)
Required on Helper companions: fill the triangle — Principle → Model → Prediction/Answer. Next Vortex must use this Tool gained. Span grows by at most one. Click the Vortex label for climb rules.
Brand-new
Tool gained: posts = gaps + 1 (fence rule).
- Principle. Posts and gaps alternate on a fence. With both ends included, posts = gaps + 1.
- Model. Length ≈ gaps × spacing; posts = gaps + 1.
- Prediction / Answer. Eight lanterns at both ends means seven gaps; on 21 m, spacing is 3 m. Hang them for a real job — not a naked n−1 drill.
1. Tool / weapon
Fence rule: posts = gaps + 1. If you need 12 lanterns with one gap between each, you need 11 gaps — so length ≈ 11 × spacing. The “weapon” is the +1 that stops off-by-one.
2. Poor explanation → rewrite
Book-style dump: “The number of posts is one more than the number of intervals.” No picture of why.
Our rewrite: Walk the fence. Every time you leave a post you cross a gap; the last post has no gap after it. Gaps are the walking; posts are the stops. Stops = walks + 1.
3. Fake → real
Fake
“A fence has n posts. How many gaps? Answer: n−1.” No job, no length, no reason to care.
Real
You hang 8 lanterns evenly along 21 m of railing, lanterns at both ends. Spacing = 21 ÷ 7 = 3 m. Tool used: gaps = lanterns − 1.
How the fake becomes real
The naked “n posts → n−1 gaps” is the same arithmetic as the lantern job. The real job supplies a length and a purpose; the fake only drills the symbol.
Real companion example: When the circle keeps turning